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%I #15 Sep 08 2022 08:45:30
%S 1,3,6,14,32,72,160,352,768,1664,3584,7680,16384,34816,73728,155648,
%T 327680,688128,1441792,3014656,6291456,13107200,27262976,56623104,
%U 117440512,243269632,503316480,1040187392,2147483648,4429185024
%N Second differences of A129952.
%C First differences of A129953: a(n) = A129953(n+1) - A129953(n).
%C Essentially the same as A078836: a(n) = A078836(n+4) for n > 1.
%H Vincenzo Librandi, <a href="/A129954/b129954.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F a(0) = 1, a(1) = 3; for n > 1, a(n) = (n+4)*2^(n-2).
%F G.f.: (1-x)*(1-2*x^2)/(1-2*x)^2.
%F Binomial transform of [1, 2, 1, 4, 1, 6, 1, 8, ...]. - _Gary W. Adamson_, Sep 29 2007
%o (Magma) m:=16; S:=&cat[ [ 1, 2*i ]: i in [0..m] ]; T:=[ &+[ Binomial(j-1, k-1)*S[k]: k in [1..j] ]: j in [1..2*m] ]; U:=[ T[n+1]-T[n]: n in[1..2*m-1] ]; [ U[n+1]-U[n]: n in[1..2*m-2] ]; // _Klaus Brockhaus_, Jun 17 2007
%o (PARI) {m=29; print1(1, ",", 3, ","); for(n=2, m, print1((n+4)*2^(n-2), ","))} \\ _Klaus Brockhaus_, Jun 17 2007
%Y Cf. A129952, A129953, A078836.
%K nonn,easy
%O 0,2
%A _Paul Curtz_, Jun 10 2007
%E Edited and extended by _Klaus Brockhaus_, Jun 17 2007
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